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Extended construction heuristics

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Optimization by GRASP

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Abstract

In Chapter 3, we considered cardinality-based and quality-based adaptive greedy algorithms as a generalization of greedy algorithms. Next, we presented semi-greedy algorithms that are obtained by randomizing adaptive greedy algorithms and constitute the main foundation for developing the construction phase of GRASP heuristics. In this chapter, we consider enhancements, extensions, and variants of greedy randomized adaptive construction procedures such as Reactive GRASP, the probabilistic choice of the construction parameter α, random plus greedy and sampled greedy constructions, cost perturbations, bias functions, principles of intelligent construction based on memory and learning, the proximate optimality principle and local search applied to partially constructed solutions, and pattern-based construction strategies using vocabulary building or data mining.

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References

  • R. Agrawal and R. Srikant. Fast algorithms for mining association rules. In Proceedings of the 20th International Conference on Very Large Data Bases, pages 487–499. Morgan Kaufmann Publishers, 1994.

    Google Scholar 

  • D. Aloise and C.C. Ribeiro. Adaptive memory in multistart heuristics for multicommodity network design. Journal of Heuristics, 17:153–179, 2011.

    MATH  Google Scholar 

  • G.A. Alvarez-Perez, J.L. González-Velarde, and J.W. Fowler. Crossdocking – Just in time scheduling: An alternative solution approach. Journal of the Operational Research Society, 60:554–564, 2008.

    MATH  Google Scholar 

  • R. Alvarez-Valdes, F. Parreño, and J.M. Tamarit. A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems. Journal of the Operational Research Society, 56:414–425, 2004.

    MATH  Google Scholar 

  • R. Alvarez-Valdes, F. Parreño, and J.M. Tamarit. Reactive GRASP for the strip-packing problem. Computers & Operations Research, 35:1065–1083, 2008b.

    Google Scholar 

  • K.P. Anagnostopoulos, P.D. Chatzoglou, and S. Katsavounis. A reactive greedy randomized adaptive search procedure for a mixed integer portfolio optimization problem. Managerial Finance, 36:1057–1065, 2010.

    Google Scholar 

  • V.A. Armentano and O.C.B. Araujo. GRASP with memory-based mechanisms for minimizing total tardiness in single machine scheduling with setup times. Journal of Heuristics, 12:427–446, 2006.

    Google Scholar 

  • L. Bahiense, G.C. Oliveira, M. Pereira, and S. Granville. A mixed integer disjunctive model for transmission network expansion. IEEE Transactions on Power Systems, 16:560–565, 2001.

    Google Scholar 

  • H. Barbalho, I. Rosseti, S.L. Martins, and A. Plastino. A hybrid data mining GRASP with path-relinking. Computers & Operations Research, 40:3159–3173, 2013.

    MATH  Google Scholar 

  • J.F. Bard, Y. Shao, and A.I. Jarrah. A sequential GRASP for the therapist routing and scheduling problem. Journal of Scheduling, 17:109–133, 2014.

    MathSciNet  MATH  Google Scholar 

  • J.E. Beasley. An algorithm for set-covering problems. European Journal of Operational Research, 31:85–93, 1987.

    MathSciNet  MATH  Google Scholar 

  • J.E. Beasley. OR-Library: Distributing test problems by electronic mail. Journal of the Operational Research Society, 41:1069–1072, 1990a.

    Google Scholar 

  • J.E. Beasley. A Lagrangean heuristic for set-covering problems. Naval Research Logistics, 37:151–164, 1990b.

    Google Scholar 

  • J.E. Beasley. Lagrangean relaxation. In C.R. Reeves, editor, Modern heuristic techniques for combinatorial problems, pages 243–303. Blackwell Scientific Publications, Oxford, 1993.

    Google Scholar 

  • D. Berger, B. Gendron, J.-Y Potvin, S. Raghavan, and P. Soriano. Tabu search for a network loading problem with multiple facilities. Journal of Heuristics, 6:253–267., 2000.

    Google Scholar 

  • S. Binato and G.C. Oliveira. A reactive GRASP for transmission network expansion planning. In C.C. Ribeiro and P. Hansen, editors, Essays and surveys in metaheuristics, pages 81–100. Kluwer Academic Publishers, Boston, 2002.

    Google Scholar 

  • S. Binato, W.J. Hery, D. Loewenstern, and M.G.C. Resende. A GRASP for job shop scheduling. In C.C. Ribeiro and P. Hansen, editors, Essays and surveys in metaheuristics, pages 59–79. Kluwer Academic Publishers, Boston, 2002.

    Google Scholar 

  • M. Boudia, M.A.O. Louly, and C. Prins. A reactive GRASP and path relinking for a combined production–distribution problem. Computers & Operations Research, 34:3402–3419, 2007.

    MATH  Google Scholar 

  • J.L. Bresina. Heuristic-biased stochastic sampling. In Proceedings of the Thirteenth National Conference on Artificial Intelligence, pages 271–278, Portland, 1996. Association for the Advancement of Artificial Intelligence.

    Google Scholar 

  • S.I. Butenko, C.W. Commander, and P.M. Pardalos. A GRASP for broadcast scheduling in ad-hoc TDMA networks. In Proceedings of the International Conference on Computing, Communications, and Control Technologies, volume 5, pages 322–328, Austin, 2004.

    Google Scholar 

  • S.A. Canuto, M.G.C. Resende, and C.C. Ribeiro. Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks, 38:50–58, 2001.

    MathSciNet  MATH  Google Scholar 

  • S. Casey and J. Thompson. GRASPing the examination scheduling problem. In E. Burke and P. De Causmaecker, editors, Practice and theory of automated timetabling IV, volume 2740 of Lecture Notes in Computer Science, pages 232–244. Springer, Berlin, 2003.

    Google Scholar 

  • I. Charon and O. Hudry. The noising method: A new method for combinatorial optimization. Operations Research Letters, 14:133–137, 1993.

    MathSciNet  MATH  Google Scholar 

  • I. Charon and O. Hudry. The noising methods: A survey. In C.C. Ribeiro and P. Hansen, editors, Essays and surveys in metaheuristics, pages 245–261. Kluwer Academic Publishers, Boston, 2002.

    Google Scholar 

  • C.W. Commander, S.I. Butenko, P.M. Pardalos, and C.A.S. Oliveira. Reactive GRASP with path relinking for broadcast scheduling. In Proceedings of the 40th Annual International Telemetry Conference, pages 792–800, San Diego, 2004.

    Google Scholar 

  • C. Cotta and A.J. Fernández. A hybrid GRASP–evolutionary algorithm approach to Golomb ruler search. In X. Yao, E.K. Burke, J.A. Lozano, J. Smith, J.J. Merelo-Guervós, J.A. Bullinaria, J.E. Rowe, P. Tiňo, A. Kabán, and H.-P. Schwefel, editors, Parallel Problem Solving from Nature, volume 3242 of Lecture Notes in Computer Science, pages 481–490. Springer, Berlin, 2004.

    Google Scholar 

  • G.L. Cravo, G.M. Ribeiro, and L.A.N. Lorena. A greedy randomized adaptive search procedure for the point-feature cartographic label placement. Computers & Geosciences, 34:373–386, 2008.

    Google Scholar 

  • S. Das and S.M. Idicula. Application of reactive GRASP to the biclustering of gene expression data. In Proceedings of the International Symposium on Biocomputing, page 14, Calicut, 2010. ACM.

    Google Scholar 

  • H. Delmaire, J.A. Díaz, E. Fernández, and M. Ortega. Reactive GRASP and tabu search based heuristics for the single source capacitated plant location problem. INFOR, 37:194–225, 1999.

    MATH  Google Scholar 

  • X. Delorme, X. Gandibleux, and J. Rodriguez. GRASP for set packing problems. European Journal of Operational Research, 153:564–580, 2004.

    MathSciNet  MATH  Google Scholar 

  • Y. Deng and J.F. Bard. A reactive GRASP with path relinking for capacitated clustering. Journal of Heuristics, 17:119–152, 2011.

    MATH  Google Scholar 

  • Y. Deng, J.F. Bard, G.R. Chacon, and J. Stuber. Scheduling back-end operations in semiconductor manufacturing. IEEE Transactions on Semiconductor Manufacturing, 23:210–220, 2010.

    Google Scholar 

  • S. Dharan and A.S. Nair. Biclustering of gene expression data using reactive greedy randomized adaptive search procedure. BMC Bioinformatics, 10 (Suppl 1):S27, 2009.

    Google Scholar 

  • A. Duarte and R. Martí. Tabu search and GRASP for the maximum diversity problem. European Journal of Operational Research, 178:71–84, 2007.

    MathSciNet  MATH  Google Scholar 

  • M. Essafi, X. Delorme, and A. Dolgui. A reactive GRASP and path relinking for balancing reconfigurable transfer lines. International Journal of Production Research, 50:5213–5238, 2012.

    Google Scholar 

  • T.A. Feo and M.G.C. Resende. A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, 8:67–71, 1989.

    MathSciNet  MATH  Google Scholar 

  • M.L. Fisher. The Lagrangean relaxation method for solving integer programming problems. Management Science, 50:1861–1871, 2004.

    Google Scholar 

  • C. Fleurent and F. Glover. Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS Journal on Computing, 11:198–204, 1999.

    MathSciNet  MATH  Google Scholar 

  • F. Glover and M. Laguna. Tabu search. Kluwer Academic Publishers, Boston, 1997.

    MATH  Google Scholar 

  • F. Glover, M. Laguna, and R. Martí. Fundamentals of scatter search and path relinking. Control and Cybernetics, 39:653–684, 2000.

    MathSciNet  MATH  Google Scholar 

  • M.X. Goemans and D.P. Williamson. The primal dual method for approximation algorithms and its application to network design problems. In D. Hochbaum, editor, Approximation algorithms for NP-hard problems, pages 144–191. PWS Publishing Company, Boston, 1996.

    Google Scholar 

  • B. Goethals and M.J. Zaki. Advances in frequent itemset mining implementations: Introduction to FIMI03. In B. Goethals and M.J. Zaki, editors, Proceedings of the IEEE ICDM 2003 Workshop on Frequent Itemset Mining Implementations, pages 1–12, Melbourne, 2003.

    Google Scholar 

  • F.C. Gomes, P. Pardalos, C.S. Oliveira, and M.G.C. Resende. Reactive GRASP with path relinking for channel assignment in mobile phone networks. In Proceedings of the 5th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pages 60–67, Rome, 2001. ACM Press.

    Google Scholar 

  • G. Grahne and J. Zhu. Efficiently using prefix-trees in mining frequent itemsets, 2003. URL http://bit.ly/1qxiKbl. Last visited on April 16, 2016.

  • J. Han, J. Pei, and Y. Yin. Mining frequent patterns without candidate generation. In Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data, pages 1–12, Dallas, 2000. ACM.

    Google Scholar 

  • J. Han, M. Kamber, and J. Pei. Data mining: Concepts and techniques. Morgan Kaufmann Publishers, San Francisco, 3rd edition, 2011.

    MATH  Google Scholar 

  • M. Held and R.M. Karp. The traveling-salesman problem and minimum spanning trees. Operations Research, 18:1138–1162, 1970.

    MathSciNet  MATH  Google Scholar 

  • M. Held and R.M. Karp. The traveling-salesman problem and minimum spanning trees: Part II. Mathematical Programming, 1:6–25, 1971.

    MathSciNet  MATH  Google Scholar 

  • M. Held, P. Wolfe, and H.P. Crowder. Validation of subgradient optimization. Mathematical Programming, 6:62–88, 1974.

    MathSciNet  MATH  Google Scholar 

  • E.H. Kampke, J.E.C. Arroyo, and A.G. Santos. Reactive GRASP with path relinking for solving parallel machines scheduling problem with resource-assignable sequence dependent setup times. In Proceedings of the World Congress on Nature and Biologically Inspired Computing, pages 924–929, Coimbatore, 2009. IEEE.

    Google Scholar 

  • R. De Leone, P. Festa, and E. Marchitto. Solving a bus driver scheduling problem with randomized multistart heuristics. International Transactions in Operational Research, 18:707–727, 2011.

    MathSciNet  MATH  Google Scholar 

  • M. Luis, S. Salhi, and G. Nagy. A guided reactive GRASP for the capacitated multi-source Weber problem. Computers & Operations Research, 38:1014–1024, 2011.

    MathSciNet  MATH  Google Scholar 

  • C.L.B. Maia, R.A.F. Carmo, F.G. Freitas, G.A.L. Campos, and J.T. Souza. Automated test case prioritization with reactive GRASP. Advances in Software Engineering, 2010, 2010. doi: 10.1155/2010/428521. Article ID 428521.

    Google Scholar 

  • R. Martí, M.G.C. Resende, and C.C. Ribeiro. Multi-start methods for combinatorial optimization. European Journal of Operational Research, 226:1–8, 2013a.

    Google Scholar 

  • B. Melián, M. Laguna, and J.A. Moreno-Pérez. Capacity expansion of fiber optic networks with WDM systems: Problem formulation and comparative analysis. Computers & Operations Research, 31:461–472, 2004.

    MATH  Google Scholar 

  • L.F. Morán-Mirabal, J.L. González-Velarde, and M.G.C. Resende. Randomized heuristics for the family traveling salesperson problem. International Transactions in Operational Research, 21:41–57, 2014.

    MathSciNet  MATH  Google Scholar 

  • S. Orlando, P. Palmerini, and R. Perego. Adaptive and resource-aware mining of frequent sets. In Proceedings of the 2002 IEEE International Conference on Data Mining, pages 338–345, Maebashi City, 2002. IEEE.

    Google Scholar 

  • F. Parreño, R. Alvarez-Valdes, J.M. Tamarit, and J.F. Oliveira. A maximal-space algorithm for the container loading problem. INFORMS Journal on Computing, 20:412–422, 2008.

    MathSciNet  MATH  Google Scholar 

  • R.A. Patterson, H. Pirkul, and E. Rolland. A memory adaptive reasoning technique for solving the capacitated minimum spanning tree problem. Journal of Heuristics, 5:159–180, 1999.

    MATH  Google Scholar 

  • L.S. Pessoa, M.G.C. Resende, and C.C. Ribeiro. Experiments with the LAGRASP heuristic for set k-covering. Optimization Letters, 5:407–419, 2011.

    MathSciNet  MATH  Google Scholar 

  • L.S. Pessoa, M.G.C. Resende, and C.C. Ribeiro. A hybrid Lagrangean heuristic with GRASP and path-relinking for set k-covering. Computers & Operations Research, 40:3132–3146, 2013.

    MathSciNet  MATH  Google Scholar 

  • A. Plastino, E.R. Fonseca, R. Fuchshuber, S.L. Martins, A.A. Freitas, M. Luis, and S. Salhi. A hybrid data mining metaheuristic for the p-median problem. In H. Park, S. Parthasarathy, H. Liu, and Z. Obradovic, editors, Proceedings of the 9th SIAM International Conference on Data Mining, pages 305–316, Sparks, 2009. SIAM.

    Google Scholar 

  • A. Plastino, R. Fuchshuber, S.L. Martins, A.A. Freitas, and S. Salhi. A hybrid data mining metaheuristic for the p-median problem. Statistical Analysis and Data Mining, 4:313–335, 2011.

    MathSciNet  MATH  Google Scholar 

  • A. Plastino, H. Barbalho, L.F.M. Santos, R. Fuchshuber, and S.L. Martins. Adaptive and multi-mining versions of the DM-GRASP hybrid metaheuristic. Journal of Heuristics, 20:39–74, 2014.

    Google Scholar 

  • M. Prais and C.C. Ribeiro. Parameter variation in GRASP implementations. In C.C. Ribeiro and P. Hansen, editors, Extended Abstracts of the Third Metaheuristics International Conference, pages 375–380, Angra dos Reis, 1999.

    Google Scholar 

  • M. Prais and C.C. Ribeiro. Reactive GRASP: An application to a matrix decomposition problem in TDMA traffic assignment. INFORMS Journal on Computing, 12:164–176, 2000a.

    Google Scholar 

  • M. Prais and C.C. Ribeiro. Parameter variation in GRASP procedures. Investigación Operativa, 9:1–20, 2000b.

    Google Scholar 

  • C. Prins, C. Prodhon, and R.Wolfler-Calvo. A reactive GRASP and path relinking algorithm for the capacitated location routing problem. In Proceedings of the International Conference on Industrial Engineering and Systems Management, Marrakech, 2005. I4E2. ISBN 2-9600532-0-6.

    Google Scholar 

  • P.P. Repoussis, C.D. Tarantilis, and G. Ioannou. A hybrid metaheuristic for a real life vehicle routing problem. In T. Boyanov, S. Dimova, K. Georgiev, and G. Nikolov, editors, Numerical methods and applications, volume 4310 of Lecture Notes in Computer Science, pages 247–254. Springer, Berlin, 2007.

    Google Scholar 

  • M.G.C. Resende and C.C. Ribeiro. A GRASP for graph planarization. Networks, 29:173–189, 1997.

    MATH  Google Scholar 

  • M.G.C. Resende and R.F. Werneck. A hybrid heuristic for the p-median problem. Journal of Heuristics, 10:59–88, 2004.

    MATH  Google Scholar 

  • M.G.C. Resende, L.S. Pitsoulis, and P.M. Pardalos. Approximate solution of weighted MAX-SAT problems using GRASP. In J. Gu and P.M. Pardalos, editors, Satisfiability problems, volume 35 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 393–405. American Mathematical Society, Providence, 1997.

    Google Scholar 

  • M.G.C. Resende, L.S. Pitsoulis, and P.M. Pardalos. Fortran subroutines for computing approximate solutions of MAX-SAT problems using GRASP. Discrete Applied Mathematics, 100:95–113, 2000.

    MATH  Google Scholar 

  • M.G.C. Resende, R. Martí, M. Gallego, and A. Duarte. GRASP and path relinking for the max-min diversity problem. Computers & Operations Research, 37: 498–508, 2010a.

    Google Scholar 

  • C.C. Ribeiro and M.G.C. Resende. Algorithm 797: Fortran subroutines for approximate solution of graph planarization problems using GRASP. ACM Transactions on Mathematical Software, 25:341–352, 1999.

    MATH  Google Scholar 

  • C.C. Ribeiro, E. Uchoa, and R.F. Werneck. A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS Journal on Computing, 14:228–246, 2002.

    MathSciNet  MATH  Google Scholar 

  • M.H.F. Ribeiro, V.F. Trindade, A. Plastino, and S.L. Martins. Hybridization of GRASP metaheuristic with data mining techniques. In Proceedings of the ECAI Workshop on Hybrid Metaheuristics, pages 69–78, Valencia, 2004.

    Google Scholar 

  • M.H.F. Ribeiro, A. Plastino, and S.L. Martins. Hybridization of GRASP metaheuristic with data mining techniques. Journal of Mathematical Modelling and Algorithms, 5:23–41, 2006.

    MathSciNet  MATH  Google Scholar 

  • R.Z. Ríos-Mercado and E. Fernández. A reactive GRASP for a commercial territory design problem with multiple balancing requirements. Computers & Operations Research, 36:755–776, 2009.

    MATH  Google Scholar 

  • Y. Rochat and É. Taillard. Probabilistic diversification and intensification in local search for vehicle routing. Journal of Heuristics, 1:147–167, 1995.

    MATH  Google Scholar 

  • L.F. Santos, M.H.F. Ribeiro, A. Plastino, and S.L. Martins. A hybrid GRASP with data mining for the maximum diversity problem. In M.J. Blesa, C. Blum, A. Roli, and M. Sampels, editors, Hybrid metaheuristics, volume 3636 of Lecture Notes in Computer Science, pages 116–127. Springer, Berlin, 2005.

    Google Scholar 

  • L.F. Santos, C.V. Albuquerque, S.L. Martins, and A. Plastino. A hybrid GRASP with data mining for efficient server replication for reliable multicast. In Proceedings of the 49th Annual IEEE GLOBECOM Technical Conference, pages 1–6, San Francisco, 2006. IEEE. doi: 10.1109/ GLOCOM.2006.246.

    Google Scholar 

  • L.F. Santos, S.L. Martins, and A. Plastino. Applications of the DM-GRASP heuristic: A survey. International Transactions on Operational Research, 15:387–416, 2008.

    MathSciNet  MATH  Google Scholar 

  • M. Scaparra and R. Church. A GRASP and path relinking heuristic for rural road network development. Journal of Heuristics, 11:89–108, 2005.

    MATH  Google Scholar 

  • A. Scholl, R. Klein, and W. Domschke. Pattern based vocabulary building for effectively sequencing mixed-model assembly lines. Journal of Heuristics, 4:359–381, 1998.

    MATH  Google Scholar 

  • F. Silva and D. Serra. Locating emergency services with different priorities: The priority queuing covering location problem. Journal of the Operational Research Society, 59:1229–1238, 2007.

    MATH  Google Scholar 

  • G.C. Silva, L.S. Ochi, and S.L. Martins. Experimental comparison of greedy randomized adaptive search procedures for the maximum diversity problem. In C.C. Ribeiro and S.L. Martins, editors, Experimental and efficient algorithms, volume 3059 of Lecture Notes in Computer Science, pages 498–512. Springer, Berlin, 2004.

    Google Scholar 

  • H. Takahashi and A. Matsuyama. An approximate solution for the Steiner problem in graphs. Mathematica Japonica, 24:573–577, 1980.

    MathSciNet  MATH  Google Scholar 

  • I.H. Witten, E. Frank, and M.A. Hall. Data mining: Practical machine learning tools and techniques. Morgan Kaufmann, San Francisco, 3rd edition, 2011.

    Google Scholar 

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Authors and Affiliations

  1. Modeling and Optimization Group (MOP), Amazon.com, Inc., Seattle, WA, USA

    Mauricio G. C. Resende

  2. Instituto de Ciência da Computação, Universidade Federal Fluminense, Niterói, Rio de Janeiro, Brazil

    Celso C. Ribeiro

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  1. Mauricio G. C. Resende
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Resende, M.G.C., Ribeiro, C.C. (2016). Extended construction heuristics. In: Optimization by GRASP. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6530-4_7

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